Answer:
This is slope-intercept form: y = (-3/4)x + 3
The slope is: -3/4
The y-intercept is: 3
Step-by-step explanation:
3x + 4y - 12 = 0
Isolate y
3x - 3x + 4y -12 + 12 = -3x + 12
Simplify
4y = -3x + 12
Divide 4 on each side to get y by itself
4y/4 = -3x/4 + 12/4
Simplify
y = (-3/4)x + 3
This is slope-intercept form: y = (-3/4)x + 3
The slope is: -3/4
The y-intercept is: 3
Label the 3 distinct sides of the box. I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:
ab=54 in^2
ac=90 in^2
bc=60 in^2
Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c. Then the volume of the box is a*b*c.
Example: bc = 90, but c = 60/b. You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.
Continuing this procedure, I determined that a=9, b=6 and c=10. Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)
Answer:
![\dfrac{x}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B4%7D)
C is correct.
Step-by-step explanation:
At a picnic,
Number of adults is 3 times as number of children.
Number of women is twice as number of men.
Total number of men, women and children at the picnic be x
Let number of children be c
Let number of men be m
Let number of women be w
# Number of women is twice as number of men, w = 2m
# Number of adults is 3 times as number of children, w + m = 3c
2m + m = 3c (∴ w=2m )
c = m
Total number of men, women and children at the picnic be x
∵ c + m + w = x
m + m + 2m = x
4m = x
Number of men, ![m=\dfrac{x}{4}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bx%7D%7B4%7D)
Hence, The total number of men will be ![\dfrac{x}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B4%7D)
Answer: 475.59 meters .
Step-by-step explanation:
The correct equation is the following:
For this exercise you need to use the Quadratic formula:
![x = \frac{-b\±\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In this case you can identify that the values of "a", "b" and "c" are:
![a=-0.02\\\\b=9.5\\\\c=5.6](https://tex.z-dn.net/?f=a%3D-0.02%5C%5C%5C%5Cb%3D9.5%5C%5C%5C%5Cc%3D5.6)
Now you must substitute these values into the Quadratic formula and then evaluate. You get:
![x=\frac{-9.5\±\sqrt{(9.5)^2-4(-0.02)(5.6)}}{2(-0.02)}\\\\x_1=475.588\\x_2=-0.588](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-9.5%5C%C2%B1%5Csqrt%7B%289.5%29%5E2-4%28-0.02%29%285.6%29%7D%7D%7B2%28-0.02%29%7D%5C%5C%5C%5Cx_1%3D475.588%5C%5Cx_2%3D-0.588)
Choose the positive one and round it to the nearest hundreth:
![x_1\approx 475.59](https://tex.z-dn.net/?f=x_1%5Capprox%20475.59)
Answer:
a - a or (a +(-a))
Step-by-step explanation:
A negative plus a positive is always zero if they have the same variable.